Jim concludes:
BTW, if this story is revealing, that indicates (once again) that game theory can say something about the world, as long as we don't obsess with equilibrium situations (Nash or otherwise).
I would have rather said "game theory can say something about the world, so long as we are careful about specifying the context within which equilibrium might arise." Without some notion of equilibrium, anything feasible can happen in any given setting, and if that's all you can say, then game theory--or any other positive social theory, for that matter--doesn't have anything useful to say about the world. Equilibrium is, of itself, not all that restrictive an idea (equilibria can evolve continually, for example); it just provides a focal point for analysis. And while I'm at it, a couple of observations about the repeated PD problem for what they're worth: Trigger strategies, or more generally "optimal penal codes," if credible, turn the supergame corresponding to the indefinitely repeated PD game into a coordination game. So do norms of reciprocating behavior. Laws and states don't solve prisoners' dilemma problems of themselves--after all, laws can be broken and state actors often don't do what they're "supposed" to do--they just change the context within which prisoners' dilemmas are played. One possibility is that they create a connected chain of prisoners' dilemma-like games (in which each game's payoff structure depends on the strategies chosen in another game) which again creates the possibility of turning all of these into interdependent coordination games. A characteristic feature of coordination games is that they have multiple, Pareto-rankable equilibria. You could get the cooperative outcome, or you could get cruddier outcomes, all the way down to perpetual mutual "defection" or the "war of all against all." Thus it might be that the ultimate social problem, once you get past the Hobbesian state of nature, is most appropriately represented by a coordination game. Gil Gil
